The dead suspect, identified as Tamerlan Tsarnaev, aged 26, had an explosive device strapped to his chest and law enforcement sources warned that his brother might have something similar.
All Boston residents were asked to stay at home as day broke and public transport was closed down.
"We believe this to be a terrorist," said Boston Police Commissioner Edward Davis. "We believe this to be a man who's come here to kill people. We need to get him in custody."
Law enforcement officials told NBC News that both men had international ties, had military experience and had lived in the United States for more than a year.
Media reports said the brothers might have come from near the restive Russian region of Chechnya.
It emerged early today that Tamerlan Tsarnaev had posted online that he didn't have a "single American friend".
"I just don't understand them."
He was reported to be a former engineering student who was into boxing and martial arts.
Earlier, heavily armed police and SWAT teams yelled at residents to "get the [expletive] inside" as explosions and gunshots sounded during the dramatic car pursuit.
The chase and shootings came after two bombs at the Boston Marathon finish line killed three people and wounded more than 180 others.
More than 9000 law enforcement officers are in Boston investigating the bombing.
The FBI earlier yesterday issued photographs of two men they believed were suspects - Tamerlan, wearing a black hat, and Dzhokhar, wearing a white hat.
About six hours after the bombing, around 10.30pm, a 7 Eleven store in suburban Cambridge was robbed, apparently by Dzhokhar.
A short time later, a campus police officer at the nearby Massachusetts Institute of Technology died after being shot several times in his patrol car while responding to a report of a disturbance.
As armed police descended on Building 32 on the campus, which houses computer science laboratories and the department of philosophy, the two suspects carjacked a nearby Mercedes SUV.
They told the driver of the car they were the "Boston bombers", police sources said.
They released its owner at a petrol station, triggering a chase into Watertown, a residential neighbourhood just west of Boston, during which explosives were thrown from the vehicle at chasing police.
During the chase and standoff, Tamerlan Tsarnaev was fatally shot.
A transit police officer was also shot and seriously injured.
Watertown resident Andrew Kitzenberg said he looked out his third-floor window and saw two young men in jackets exchanging "constant gunfire" with police officers.
The suspects had a large bomb, he told the New York Times. "They lit it, still in the middle of gunfire, and threw it."
When it exploded one of the men - identified as Tamerlan - ran towards the police officers and was tackled, while Dzhokhar drove away.
After he fled, heavily armed SWAT teams and uniformed police with guns drawn searched the area.
One police officer yelled at bystanders: "Ya gotta get outta here. There's an active shooter here with an active explosive. Go!"
The FBI agent in charge in Boston, Richard DesLauriers, said that in surveillance film shown by the agency, Tamerlan was seen setting down a backpack at the site of the second explosion.
The marathon blasts killed 8-year-old Martin Richard, 29-year-old Krystle Campbell and Lu Lingzi, a graduate student from China. Many victims lost limbs, and seven remained in critical condition.
